Geodesic
An algorithm for studying the renormalization group dynamics in the projective space
Informatics and Automation, Selected topics of mathematical physics and analysis, Tome 285 (2014), pp. 221-231.

Voir la notice de l'article provenant de la source Math-Net.Ru

The renormalization group dynamics is studied in the four-component fermionic hierarchical model in the space of coefficients that determine the Grassmann-valued density of the free measure. This space is treated as a two-dimensional projective space. If the renormalization group parameter is greater than $1$, then the only attracting fixed point of the renormalization group transformation is defined by the density of the Grassmann $\delta$-function. Two different invariant neighborhoods of this fixed point are described, and an algorithm is constructed that allows one to classify the points on the plane according to the way they tend to the fixed point. 
@article{TRSPY_2014_285_a13,
     author = {M. D. Missarov and A. F. Shamsutdinov},
     title = {An algorithm for studying the renormalization group dynamics in the projective space},
     journal = {Informatics and Automation},
     pages = {221--231},
     publisher = {mathdoc},
     volume = {285},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2014_285_a13/}
}
TY  - JOUR
AU  - M. D. Missarov
AU  - A. F. Shamsutdinov
TI  - An algorithm for studying the renormalization group dynamics in the projective space
JO  - Informatics and Automation
PY  - 2014
SP  - 221
EP  - 231
VL  - 285
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2014_285_a13/
LA  - ru
ID  - TRSPY_2014_285_a13
ER  - 
%0 Journal Article
%A M. D. Missarov
%A A. F. Shamsutdinov
%T An algorithm for studying the renormalization group dynamics in the projective space
%J Informatics and Automation
%D 2014
%P 221-231
%V 285
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2014_285_a13/
%G ru
%F TRSPY_2014_285_a13
M. D. Missarov; A. F. Shamsutdinov. An algorithm for studying the renormalization group dynamics in the projective space. Informatics and Automation, Selected topics of mathematical physics and analysis, Tome 285 (2014), pp. 221-231. http://geodesic.mathdoc.fr/item/TRSPY_2014_285_a13/

[1] Missarov M.D., “Renormalization group and renormalization theory in $p$-adic and adelic scalar models”, Dynamical systems and statistical mechanics, Adv. Sov. Math., 3, ed. Ya.G. Sinai, Amer. Math. Soc., Providence, RI, 1991, 143–164 | MR

[2] Vladimirov V.S., Volovich I.V., Zelenov E.I., $p$-Adicheskii analiz i matematicheskaya fizika, Fizmatlit, M., 1994 | MR | Zbl

[3] Missarov M.D., “Nepreryvnyi predel v fermionnoi ierarkhicheskoi modeli”, TMF., 118:1 (1999), 40–50 | DOI | MR | Zbl

[4] Missarov M.D., “Renormalizatsionnaya gruppa v fermionnoi ierarkhicheskoi modeli v proektivnykh koordinatakh”, TMF, 173:3 (2012), 355–362 | DOI | Zbl

[5] Lerner E.Yu., Missarov M.D., “Fixed points of renormalization group for the hierarchical fermionic model”, J. Stat. Phys., 76:3–4 (1994), 805–817 | DOI | MR | Zbl

[6] Lerner E.Yu., Missarov M.D., “Globalnyi potok renormalizatsionnoi gruppy i termodinamicheskii predel v fermionnoi ierarkhicheskoi modeli”, TMF, 107:2 (1996), 201–212 | DOI | MR | Zbl

[7] Missarov M.D., “RG-invariantnye krivye v fermionnoi ierarkhicheskoi modeli”, TMF, 114:3 (1998), 323–336 | DOI | MR | Zbl

[8] Missarov M.D., “Kriticheskie yavleniya v fermionnoi ierarkhicheskoi modeli”, TMF, 117:3 (1998), 471–488 | DOI | MR | Zbl

[9] Missarov M.D., “Dynamical phenomena in the hierarchical fermionic model”, Phys. Lett. A, 253 (1999), 41–46 | DOI

[10] Missarov M.D., “Renormalization group solution of fermionic Dyson model”, Asymptotic combinatorics with application to mathematical physics, NATO Sci. Ser. II: Math. Phys. Chem., 77, eds. V.A. Malyshev, A.M. Vershik, Kluwer, Dordrecht, 2002, 151–166 | MR | Zbl